Equilibrium via vertical force balance

Steps:

• Vertical component of first tension: 410 sin(60°) = 410 × (√3/2) ≈ 355 N upward.
• Vertical component of second tension: 210 sin(10°) ≈ 210 × 0.174 = 36.5 N upward.
• Total upward force = 355 + 36.5 = 391.5 N ≈ 400 N (weight mg).
• Mass m = 400 / g = 400 / 10 = 40 kg (using g = 10 m/s²).

Why A is correct:

• Weight equals sum of vertical tension components, yielding 400 N, so m = 40 kg by W = mg.

Why the others are wrong:

• B overestimates mass; vertical forces sum to ~400 N, not 420 N.
• C far exceeds; would require ~900 N vertical force.
• D much too high; implies ~1400 N, ignoring actual components.

Final answer: A